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Application of Maxima and Minima
As an example, the area of a rectangular lot, expressed in terms of its length and width, may also be expressed in terms of the cost of fencing. Thus the area can be expressed as A = f(x). The common task here is to find the value of x that will give a maximum value of A. To find this value, we set dA/dx = 0.
Steps in Solving Maxima and Minima Problems
- Identify the constant, say cost of fencing.
- Identify the variable to be maximized or minimized, say area A.
- Express this variable in terms of the other relevant variable(s), say A = f(x, y).
- If the function shall consist of more than one variable, expressed it in terms of one variable (if possible and practical) using the conditions in the problem, say A = f(x).
- Differentiate and equate to zero, dA/dx = 0.
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